2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170079Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a function $f\in\cD$ to be {\em cyclic}, i.e. for $\{pf: p\text{a polynomial}\}$ to be dense in $\cD$. This allows us to prove a special case of the conjecture of Brown and Shields that a function is cyclic in $\cD$ iff it is outer and its zero set (defined appropriately) is of capacity zero.Complex VariablesFunctional Analysis30H05 (Primary); 46E20, 47A15 (Secondary)text